संकेत शब्द
Double well Potential
Plasma System
Physics Informed Neural Networks
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सार
The time-independent Schrodinger equation plays a fundamental role in describing quantum tunneling phenomena in systems governed by double-well potentials, which arise naturally as effective potentials in quantum plasma environments due to external fields and confinement effects. In this work, we employ Physics-Informed Neural Networks (PINNs) to solve one-dimensional Schrodinger equation for a symmetric double-well potential and obtain accurate ground and low-lying excited state solutions. The fully connected neural networks is used to obtain the wavefunctions, while the energy eigenvalues are treated as trainable parameters and determined through the minimization of a composite loss function enforcing the governing differential equation, boundary conditions, normalization, and orthogonality constraints. Even and odd-parity network architectures are used to directly capture symmetric and antisymmetric eigenstates. The PINNs results are validated against finite-difference matrix diagonalization technique, showing good agreement for the lowest energy levels and correctly reproducing the near-degeneracy caused by quantum tunneling between the wells. These results demonstrate that PINNs provide a flexible, accurate, and mesh-free alternative to conventional numerical techniques, making them well suited for modelling tunneling phenomena and effective quantum potentials in plasma-related systems.